一、题目：

On the sup-norm problem of automorphic forms: new counting methods

二、主讲人：

Péter Maga

三、摘要：

As it was proved by Sarnak, the supnorm of eigenfunctions of the Laplacian on a compact symmetric Riemannian manifold can be estimated from above by an appropriate power (given in terms of some invariants of the space) of their Laplace eigenvalue. Examples show that Sarnak's exponent is sharp in some cases. However, when the space has also arithmetic symmetries (i.e. Hecke operators) and we restrict to joint eigenfunctions of the Laplacian and the Hecke operators, one might expect a better exponent. Such power-savings are known for arithmetic quotients of several symmetric spaces. In the talk, I will give a brief overview of the history of the problem, and discuss some new matrix counting methods which might potentially yield the desired power-saving in some currently unsettled cases. The talk will be based on ongoing research (joint with Gergely Zábrádi).

四、主讲人简介：

Péter Maga is a research follow at Alfréd Rényi Institute of Mathematics.

五、邀请人：

黄炳荣

六、时间：

11月30日（周三）20:00-21:00

七、地点：

Zoom meeting

八、联系人：

黄炳荣，联系方式：brhuang@sdu.edu.cn

九、主办：

山东大学数学学院